"We respect Indonesia's sovereignty but we do deplore what's been done and this cannot be simply business as usual. For that reason, once all the courtesies have been extended to the Chan and Sukumaran families, our ambassador will be withdrawn for consultations."

Australia has not withdrawn ambassadors when other Australian citizens have been subjected to the death penalty, including when convicted Australian drug smuggler Van TuongNguyen was executed in Singapore in 2005.

Mr Abbott acknowledged that this was a "dark moment" in Australia's relationship with Indonesia.

"I want to stress that this is a very important relationship between Australia and Indonesia but it has suffered as a result of what's been done over the last few hours," he said.

Foreign Affairs Minister Julie Bishop said that Australia's ambassador, Paul Grigson, would return to Australia by the end of the week for consultations with the government about the future of Australia's relationship with Indonesia.

Andrew Chan and Myuran Sukumaran were executed by firing squad in April.Credit:Anta Kesuma

"The withdrawal of an ambassador is to register our displeasure at the way our citizens have been treated," Ms Bishop said.

Executing the two men was "senseless", given they had rehabilitated themselves during a decade in prison, Ms Bishop said.

Mr Abbott said he understood that Australians would be angry about Indonesia's decision to proceed with the executions but urged people not to make a bad situation worse.

"I absolutely understand people's anger," Mr Abbott said.

So I would say to people yes, you are absolutely entitled to be angry but we've got to be very careful to ensure that we do not allow our anger to make a bad situation worse

"On the other hand, we do not want to make a difficult situation worse and the relationship between Australia and Indonesia is important, remains important, will always be important, will become more important as time goes by. So I would say to people yes, you are absolutely entitled to be angry but we've got to be very careful to ensure that we do not allow our anger to make a bad situation worse."

Ms Bishop said that Australia's aid budget to Indonesia would be dealt with separately.

Opposition Leader Bill Shorten and Deputy Leader Tanya Plibersek on Wednesday afternoon echoed the government and public's condemnation of the executions, vowing to fight against the death penalty wherever it existed in the world.

He said whenever Australian leaders are abroad they should make the case against the death penalty.

"[We should] say 'this solves nothing'," Mr Shorten said.

The Opposition Leader also made it clear that Australian anger was not directed at the Indonesian people, but was aimed at their government.

"It was not justice, it was the senseless waste of two good lives," Mr Shorten said in Melbourne.

"We are disgusted at the futile act of execution of these two young Australian men."

The opposition said it was clear that the two men had been rehabilitated. It is also furious that calls for mercy had fallen on deaf ears.

"Australians have been united in pleading for mercy, pleading for clemency for the lives these two young men and we are deeply hurt and deeply troubled that those pleas for mercy have been ignored," Ms Plibersek said.

"Their families now bear the loss of these two young men for the rest of their lives, this is a life sentence for their families and friends."

The Labor opposition also backed the withdrawal of Australia's ambassador to Indonesia as well as a hold on ministerial meetings.

Mr Shorten spoke to Mr Abbott about potential options in responding to Indonesia's execution of two Australians.

"I don't hold ordinary Indonesians responsible," Mr Shorten said. "I see this as a failure in terms of the justice system in Indonesia and I see this as the wrong decision to be made."

Ms Plibersek said the good relationship with Indonesia had been put under enormous pressure in recent weeks and months.

Tightening the guidelines for the Australian Federal Police was something the Parliament could consider, Mr Shorten said.

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Mr Shorten and Ms Plibersek praised Australian diplomats, embassy staff and the Prime Minister and Foreign Minister for their efforts to save the men's lives.